(October 10, 2018 at 2:46 pm)SteveII Wrote:(October 10, 2018 at 1:59 pm)polymath257 Wrote: The logical possibility is demonstrated by the consistency of the math. That is *all* that is required to show that the concept is consistent.
Metaphysics is usually simply re-arranging preconceptions. It is flawed from the beginning. The *only* relevant questions are whether the concept of infinity is logically inconsistent (it isn't) and whether observation supports some actual infinity. I agree that we have no *positive proof* of an infinite space, for example, but the current evidence certainly allows for that possibility. But that isn't the issue. The issue is whether an actual infinity is *logically* contradictory. And the math shows that it isn't.
That we are talking about 'concrete' objects is irrelevant to the logical possibility. All that is required is an infinite extent of space (certainly a logical possibility) and concrete objects scattered in that infinite space.
Ahh--so all we need to do is declare some axiom (like the Axiom of Infinity) and PRESTO -- there exists the possibility of an infinite number of concrete objects in the real world. Got it. Glad to know your basis for your argument is so well founded.
Whether some object is concrete or not is "irrelevant"!? You don't even realize you are positing metaphysical possibilities using a discipline that the real world has no constraints upon. No wonder you couldn't come up with an article.
The fact that there is no internal contradiction means it isn't logically eliminated. So, yes, we get to assume any axiom that isn't contradictory. The *logic* isn't violated.
Metaphysics is bunk. Pure and simple. There is no such thing as valid metaphysical reasoning: only metaphysical assumptions, usually invalid ones.
I won't come up with a metaphysics article because I consider *all* metaphysics articles to be bunk. But, the math and physics articles are very clear about the *logical* possibility of an actual infinite.
The problem I have with 'concrete' objects is that I don't consider the word 'concrete' to be well defined. For example, is an electron a 'concrete object'? Give reasons for your answer. is a neutrino a 'concrete object'? is a photon? These are the *actual* objects from which the universe is built. These are the ones that matter. Whatever your vague notion of 'concreteness' is irrelevant to the actual physics. And if your metaphysics doens't allow the actual physics, then it is simply invalid.